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Is a rational function one-one or onto

This type of question, asked 5 times: 29 Jan 2023, 6 Apr 2024, 24 Jan 2025, 28 Jan 2026 S2, 6 Apr 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    29 Jan 2023

    79
    Let f:R→Rf:R \rightarrow R be a function such that f(x)=x2+2x+1x2+1f(x) =\frac{x^{2}+ 2x + 1}{x^{2}+ 1}. Then

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  2. Question 2

    6 Apr 2024

    65
    The function f(x)=x2+2x−15x2−4x+9,x∈Rf(x) =\frac{x^{2}+ 2x- 15}{x^{2}- 4x+ 9},x\in R is

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  3. Question 3

    24 Jan 2025

    127
    The function f:(−∞,∞)→(−∞,1)f:( - \infty,\infty) \rightarrow ( - \infty,1), defined by f(x)=2x−2−x2x+2−xf(x) =\frac{2^{x}-2^{-x}}{2^{x}+2^{-x}} is :

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  4. Question 4

    28 Jan 2026 S2

    58
    Given below are two statements : Statement I : The function f:R→Rf:R \rightarrow R defined by f(x)=x1+∣x∣f(x) = \frac{x}{1 + |x|} is one-one. Statement II : The function f:R→Rf:R \rightarrow R defined by f(x)=x2+4x−30x2−8x+18f(x) = \frac{x^{2} + 4x - 30}{x^{2} - 8x + 18} is many-one. In the light of the above statements, choose the correct answer from the options given below:

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  5. Question 5

    6 Apr 2026 S2

    51
    Let f:R→Rf:R \rightarrow R be defined as f(x)=2x2−3x+23x2+x+3f(x) =\frac{2x^{2}- 3x + 2}{3x^{2}+ x + 3}. Then ff is :

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